Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A 1600 kg car drives around a flat curve of radius 190 m at a constant 16 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 16 m/sr = 190 m

F_c = N

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius r_min for a curve taken at 250 km/h?

v = 250 km/ha_max = 1 m/s²

r_min = m

3.Medium

A curve of radius 150 m is banked at 20°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 150 mθ = 20°g = 9.81 m/s²

v = m/s

4.Medium

A small ball on a string of length 1.7 m moves in a horizontal circle so that the string makes a constant angle of 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.7 mθ = 30°g = 9.81 m/s²

T = s

5.Hard

A 0.6 kg ball on a light string 1.2 m long is swung in a vertical circle. At the lowest point its speed is 8 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 0.6 kgr = 1.2 mv_bottom = 8 m/sg = 9.81 m/s²

T_top = N

6.Hard

A ball on a string 1.4 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed v_min at the top for which the string just stays tight?

r = 1.4 mg = 9.81 m/s²

v_min = m/s

Answer key

1. F_c = 2156 N
2. r_min = 4823 m
3. v = 23.14 m/s
4. T = 2.434 s
5. T_top = 2.57 N
6. v_min = 3.706 m/s

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